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Bipolar Fuzzy Spatial Information: Geometry, Morphology, Spatial Reasoning

  • Chapter
Methods for Handling Imperfect Spatial Information

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 256))

Abstract

Spatial information may be endowed with a bipolarity component. Typical examples concern possible vs forbidden places for an object in space, or “opposite” spatial relations such as “possibly to the right of an object and certainly not to its left”. However, bipolarity has not been much exploited in the spatial domain yet. Moreover, imprecision has often to be taken into account as well, for instance to model vague statements such as “to the right of an object”. In this paper we propose to handle both features in the framework of bipolar fuzzy sets. We introduce some geometrical measures and mathematical morphology operations on bipolar fuzzy sets and illustrate their potential for spatial reasoning on a simple scenario in brain imaging.

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References

  1. Amgoud, L., Cayrol, C., Lagasquie-Schiez, M.C., Livet, P.: On bipolarity in argumentation frameworks. International Journal of Intelligent Systems 23(10), 1062–1093 (2008)

    Article  MATH  Google Scholar 

  2. Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  3. Atanassov, K.T.: Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s Paper Terminology Difficulties in Fuzzy Set Theory – The Case of “Intuitionistic Fuzzy Sets” Fuzzy Sets and Systems 156, 496–499 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Benferhat, S., Dubois, D., Kaci, S., Prade, H.: Bipolar Possibility Theory in Preference Modeling: Representation, Fusion and Optimal Solutions. Information Fusion 7, 135–150 (2006)

    Google Scholar 

  5. Benferhat, S., Dubois, D., Prade, H.: Modeling positive and negative information in possibility theory. International Journal of Intelligent Systems 23(10), 1094–1118 (2008)

    Article  MATH  Google Scholar 

  6. Bloch, I.: Fuzzy Relative Position between Objects in Image Processing: a Morphological Approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(7), 657–664 (1999)

    Article  Google Scholar 

  7. Bloch, I.: On Fuzzy Distances and their Use in Image Processing under Imprecision. Pattern Recognition 32(11), 1873–1895 (1999)

    Article  Google Scholar 

  8. Bloch, I.: Spatial Representation of Spatial Relationships Knowledge. In: Cohn, A.G., Giunchiglia, F., Selman, B. (eds.) 7th International Conference on Principles of Knowledge Representation and Reasoning KR 2000, Breckenridge, CO, pp. 247–258. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  9. Bloch, I.: Duality vs Adjunction and General Form for Fuzzy Mathematical Morphology. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 354–361. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Bloch, I.: Fuzzy Spatial Relationships for Image Processing and Interpretation: A Review. Image and Vision Computing 23(2), 89–110 (2005)

    Article  Google Scholar 

  11. Bloch, I.: Spatial Reasoning under Imprecision using Fuzzy Set Theory, Formal Logics and Mathematical Morphology. International Journal of Approximate Reasoning 41, 77–95 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Bloch, I.: Dilation and Erosion of Spatial Bipolar Fuzzy Sets. In: Masulli, F., Mitra, S., Pasi, G. (eds.) WILF 2007. LNCS (LNAI), vol. 4578, pp. 385–393. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Bloch, I.: An Extension of Skeleton by Influence Zones and Morphological Interpolation to Fuzzy Sets. In: International Symposium on Mathematical Morphology (ISMM 2007), Rio de Janeiro, Brazil, October 2007, pp. 3–14 (2007)

    Google Scholar 

  14. Bloch, I.: A Contribution to the Representation and Manipulation of Fuzzy Bipolar Spatial Information: Geometry and Morphology. In: Workshop on Soft Methods in Statistical and Fuzzy Spatial Information, Toulouse, France, September 2008, pp. 7–25 (2008)

    Google Scholar 

  15. Bloch, I.: Bipolar Fuzzy Mathematical Morphology for Spatial Reasoning. In: International Symposium on Mathematical Morphology ISMM 2009, Groningen, The Netherlands, vol. 5720, pp. 24–34 (August 2009)

    Google Scholar 

  16. Bloch, I.: Duality vs. Adjunction for Fuzzy Mathematical Morphology and General Form of Fuzzy Erosions and Dilations. Fuzzy Sets and Systems 160, 1858–1867 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Bloch, I.: Geometry of Spatial Bipolar Fuzzy Sets based on Bipolar Fuzzy Numbers and Mathematical Morphology. In: Di Gesù, V., Pal, S.K., Petrosino, A. (eds.) Fuzzy Logic and Applications. LNCS (LNAI), vol. 5571, pp. 237–245. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Bloch, I., Géraud, T., Maître, H.: Representation and Fusion of Heterogeneous Fuzzy Information in the 3D Space for Model-Based Structural Recognition - Application to 3D Brain Imaging. Artificial Intelligence 148, 141–175 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  19. Bloch, I., Heijmans, H., Ronse, C.: Mathematical Morphology. In: Aiello, M., Pratt-Hartman, I., van Benthem, J. (eds.) Handbook of Spatial Logics, ch. 13, pp. 857–947. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Bloch, I., Maître, H.: Fuzzy Mathematical Morphologies: A Comparative Study. Pattern Recognition 28(9), 1341–1387 (1995)

    Article  MathSciNet  Google Scholar 

  21. Bonnefon, J.F.: Two routes for bipolar information processing, and a blind spot in between. International Journal of Intelligent Systems 23(9), 923–929 (2008)

    Article  MATH  Google Scholar 

  22. Bustince, H., Burillo, P.: Vague Sets are Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 79, 403–405 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Caferra, R., Peltier, N.: Accepting/rejecting propositions from accepted/rejected propositions: A unifying overview. International Journal of Intelligent Systems 23(10), 999–1020 (2008)

    Article  MATH  Google Scholar 

  24. Chaira, T., Ray, A.K.: A New Measure using Intuitionistic Fuzzy Set Theory and its Application to Edge Detection. Applied Soft Computing Journal 8(2), 919–927 (2008)

    Article  Google Scholar 

  25. Charlier, N., De Tré, G., Gautama, S., Bellens, R.: A Twofold Fuzzy Region Model for Imprecise Quality Control of Geographic Information. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2008, Part I. LNCS, vol. 5072, pp. 647–662. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  26. Colliot, O., Camara, O., Bloch, I.: Integration of Fuzzy Spatial Relations in Deformable Models - Application to Brain MRI Segmentation. Pattern Recognition 39, 1401–1414 (2006)

    Article  Google Scholar 

  27. Cornelis, C., Deschrijver, G., Kerre, E.: Implication in Intuitionistic Fuzzy and Interval-Valued Fuzzy Set Theory: Construction, Classification, Application. International Journal of Approximate Reasoning 35, 55–95 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  28. Cornelis, C., Kerre, E.: Inclusion Measures in Intuitionistic Fuzzy Sets. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 345–356. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  29. Couto, P., Bustince, H., Melo-Pinto, P., Pagola, M., Barrenechea, E.: Image Segmentation using A-IFSs. In: IPMU 2008, Malaga, Spain, pp. 1620–1627 (2008)

    Google Scholar 

  30. De Baets, B.: Generalized Idempotence in Fuzzy Mathematical Morphology. In: Kerre, E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing. Studies in Fuzziness and Soft Computing, vol. 52, pp. 58–75. Physica Verlag, Springer (2000)

    Google Scholar 

  31. Deng, T.-Q., Heijmans, H.: Grey-Scale Morphology Based on Fuzzy Logic. Journal of Mathematical Imaging and Vision 16, 155–171 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  32. Deschrijver, G., Cornelis, C., Kerre, E.: On the Representation of Intuitionistic Fuzzy t-Norms and t-Conorms. IEEE Transactions on Fuzzy Systems 12(1), 45–61 (2004)

    Article  MathSciNet  Google Scholar 

  33. Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminology Difficulties in Fuzzy Set Theory – The Case of “Intuitionistic Fuzzy Sets”. Fuzzy Sets and Systems 156, 485–491 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  34. Dubois, D., Kaci, S., Prade, H.: Bipolarity in Reasoning and Decision, an Introduction. In: International Conference on Information Processing and Management of Uncertainty, IPMU 2004, Perugia, Italy, pp. 959–966 (2004)

    Google Scholar 

  35. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New-York (1980)

    MATH  Google Scholar 

  36. Dubois, D., Prade, H.: A Bipolar Possibilistic Representation of Knowledge and Preferences and Its Applications. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 1–10. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  37. Dubois, D., Prade, H.: An introduction to bipolar representations of information and preference. International Journal of Intelligent Systems 23(8), 865–866 (2008)

    Google Scholar 

  38. Grabisch, M., Greco, S., Pirlot, M.: Bipolar and bivariate models in multicriteria decision analysis: Descriptive and constructive approaches. International Journal of Intelligent Systems 23(9), 930–969 (2008)

    Article  MATH  Google Scholar 

  39. Heijmans, H.J.A.M., Ronse, C.: The Algebraic Basis of Mathematical Morphology – Part I: Dilations and Erosions. Computer Vision, Graphics and Image Processing 50, 245–295 (1990)

    Article  MATH  Google Scholar 

  40. Hong, D.H., Lee, S.: Some Algebraic Properties and a Distance Measure for Interval-Valued Fuzzy Numbers. Information Sciences 148(1-4), 1–10 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  41. Hudelot, C., Atif, J., Bloch, I.: Fuzzy Spatial Relation Ontology for Image Interpretation. Fuzzy Sets and Systems 159, 1929–1951 (2008)

    Article  MathSciNet  Google Scholar 

  42. Kaci, S.: Logical formalisms for representing bipolar preferences. International Journal of Intelligent Systems 23(8), 985–997 (2008)

    Article  MATH  Google Scholar 

  43. Konieczny, S., Marquis, P., Besnard, P.: Bipolarity in bilattice logics. International Journal of Intelligent Systems 23(10), 1046–1061 (2008)

    Article  MATH  Google Scholar 

  44. Malek, M.R.: Spatial Object Modeling in Intuitionistic Fuzzy Topological Spaces. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 427–434. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  45. Malek, M.R.: Intuitionistic Fuzzy Spatial Relationships in Mobile GIS Environment. In: Masulli, F., Mitra, S., Pasi, G. (eds.) WILF 2007. LNCS (LNAI), vol. 4578, pp. 313–320. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  46. Maragos, P.: Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems. Journal of Mathematical Imaging and Vision 22, 333–353 (2005)

    Article  MathSciNet  Google Scholar 

  47. Nachtegael, M., Kerre, E.E.: Classical and Fuzzy Approaches towards Mathematical Morphology. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, Studies in Fuzziness and Soft Computing, ch. 1, pp. 3–57. Physica-Verlag, Springer (2000)

    Google Scholar 

  48. Nachtegael, M., Sussner, P., Mélange, T., Kerre, E.: Some Aspects of Interval-Valued and Intuitionistic Fuzzy Mathematical Morphology. In: IPCV 2008 (2008)

    Google Scholar 

  49. Da Silva Neves, R., Livet, P.: Bipolarity in human reasoning and affective decision making. International Journal of Intelligent Systems 23(8), 898–922 (2008)

    Article  Google Scholar 

  50. Öztürk, M., Tsoukias, A.: Bipolar preference modeling and aggregation in decision support. International Journal of Intelligent Systems 23(9), 970–984 (2008)

    Article  MATH  Google Scholar 

  51. Raufaste, E., Vautier, S.: An evolutionist approach to information bipolarity: Representations and affects in human cognition. International Journal of Intelligent Systems 23(8), 878–897 (2008)

    Article  Google Scholar 

  52. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)

    MATH  Google Scholar 

  53. Sinha, D., Dougherty, E.R.: Fuzzification of Set Inclusion: Theory and Applications. Fuzzy Sets and Systems 55, 15–42 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  54. Soille, P.: Morphological Image Analysis. Springer, Berlin (1999)

    MATH  Google Scholar 

  55. Szmidt, E., Kacprzyk, J.: Distances between Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 114(3), 505–518 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  56. Szmidt, E., Kacprzyk, J.: Entropy for Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  57. Vlachos, I.K., Sergiadis, G.D.: Intuitionistic Fuzzy Information – Applications to Pattern Recognition. Pattern Recognition Letters 28(2), 197–206 (2007)

    Article  Google Scholar 

  58. Wang, G., Li, X.: The Applications of Interval-Valued Fuzzy Numbers and Interval-Distribution Numbers. Fuzzy Sets and Systems 98(3), 331–335 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  59. Waxman, S.G.: Correlative Neuroanatomy, 24th edn. McGraw-Hill, New York (2000)

    Google Scholar 

  60. Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Information Sciences 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Télécom ParisTech, CNRS LTCI, Paris, France

    Isabelle Bloch

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  1. Isabelle Bloch
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Editors and Affiliations

  1. IGM Université Paris Est, Champs-sur-Marne, France

    Robert Jeansoulin

  2. LSIS UMR CNRS, Marseille, France

    Odile Papini

  3. Université Paul Sabatier, Toulouse, France

    Henri Prade

  4. Ghent University, Ghent, Belgium

    Steven Schockaert

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Bloch, I. (2010). Bipolar Fuzzy Spatial Information: Geometry, Morphology, Spatial Reasoning. In: Jeansoulin, R., Papini, O., Prade, H., Schockaert, S. (eds) Methods for Handling Imperfect Spatial Information. Studies in Fuzziness and Soft Computing, vol 256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14755-5_4

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  • DOI: https://doi.org/10.1007/978-3-642-14755-5_4

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